Next: MC123 Introduction to Newtonian
Up: Year 1
Previous: MC117 Operating Systems and
MC120 Vectors and Geometry
| Credits: 10 |
Convenor: Dr. M. Walmsley |
Semester: 1 (weeks 1 to 6) |
| Prerequisites: |
essential: A-level Mathematics |
desirable: |
| Assessment: |
Coursework and/or tests: 20% |
One and a half hour exam in January: 80% |
| Lectures: |
18 |
Classes: |
none |
| Tutorials: |
6 |
Private Study: |
51 |
| Labs: |
none |
Seminars: |
none |
| Project: |
none |
Other: |
6 |
| Total: |
75 |
|
|
Explanation of Pre-requisites
Students must have good core A-level skills,
most especially in algebra and trigonometry.
Course Description
A knowledge of vectors provides and essential tool for the discussion of
many problems in applied mathematics and in particular those involving
force and motion. Problems of a geometric nature, in particular those
relating to lines and planes, can frequently be solved easily with a
vector approach. Following a brief description of familiar geometrical
ideas in two dimensional space, the module will continue with a presentation
of the algebra of vectors in three dimensional space. This will include
the introduction of the scalar, vector and triple products with particular
application to the geometry of lines and planes.
Aims
The module aims to provide students with a thorough knowledge of vector
algebra, so that they can see the advantage of their use in the discussion
of certain types of geometric problems. Coursework will emphasize the
importance of providing clear, concise and well explained mathematical
proofs.
Objectives
By the end of the module students should be
- able to do basic vector algebra using scalar, vector and
triple products;
- able to use vectors in the description of lines and planes;
- able to solve simple geometric problems with the aid of
vector methods;
- developing good written mathematical presentation skills.
Transferable Skills
This module will develop the following useful skills:
- problem solving;
- written mathematical presentation;
- appreciation of the importance of a logical mathematical
argument
Syllabus
- 1.
- Revision and extension of simple two dimensional coordinate geometry:
simple curves, parametrisation of coordinates, polar coordinates.
- 2.
- Vectors and scalars: addition law, position vector, simple geometrical
applications.
- 3.
- Vectors in Cartesian form: length, equation of a straight line.
- 4.
- Scalar product of two vectors: properties, application to the
equation of a plane, problems involving lines and planes.
- 5.
- Vector product: properties, applications.
- 6.
- Vector triple product: scalar triple product, vector triple
product, geometrical and algebraic applications.
Reading list
Background:
E.A. Maxwell,
Coordinate Geometry with Vectors and Tensors,
Clarendon Press, Oxford.
D.C. Murdoch,
Analytic Geometry with an Introduction to Vectors and Matrices,
Wiley.
C.E. Weatherburn,
Elementary Vector Analysis,
Bell and Sons.
E. Wolstenholme,
Elementary Vectors,
Pergamon.
P.C. Matthews,
Vector Calculus,
Springer.
M.R. Spiegel,
Vector Calculus,
Schaum Outline Series.
Details of Assessment
The 20 % coursework mark for the module will arise from a 50 minute test
(giving 10%) and the weekly problem sheet work (giving another 10%).
During the January 1999 examination period there will be a one and a half
hour paper of four questions, which will give 80% of the module mark.
Next: MC123 Introduction to Newtonian
Up: Year 1
Previous: MC117 Operating Systems and
Roy L. Crole
10/22/1998